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An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)
Responses

−5x−y=−1
negative 5 x minus y equals negative 1

y=−5x+1
y equals negative 5 x plus 1

y=5x+1
y equals 5 x plus 1

y=−5x−1
y equals negative 5 x minus 1

1 answer

To write the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) of the line.

The line passes through the points (0, 1) and (1, -4). We can calculate the slope (m) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, 1) and (1, -4):

  • \(y_1 = 1\), \(y_2 = -4\)
  • \(x_1 = 0\), \(x_2 = 1\)

Plugging in the values: \[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]

Now that we have the slope (m = -5), we can use the slope-intercept form along with one of the points to find the y-intercept (b). We can use the point (0, 1): \[ y = mx + b \] \[ 1 = -5(0) + b \] \[ 1 = b \]

Now we have the slope and the y-intercept:

  • Slope (m) = -5
  • y-intercept (b) = 1

Thus, the equation of the line in slope-intercept form is:

\[ y = -5x + 1 \]

Therefore, the correct response is: y = −5x + 1.